1. Magnetic force on a moving charge

For a charge $Q$ moving with velocity $\vec v$ in a magnetic field $\vec B$, the magnetic force is

2. Direction of magnetic force

The cross product $\vec v \times \vec B$ is always perpendicular to $\vec v$. So, the magnetic force $\vec F$ is always perpendicular to the instantaneous displacement $d\vec l$ (since displacement is along velocity direction).

3. Work done by force

The infinitesimal work done is

Since $\vec F \perp d\vec l$,

Hence,

and therefore total work done by the magnetic field is also

4. Checking options

• A: Zero $\rightarrow$ Correct
• B: $-1$ $\rightarrow$ Incorrect
• C: Infinite $\rightarrow$ Incorrect
• D: 1 $\rightarrow$ Incorrect

5. Final answer

The work done by a magnetic field on a moving charge is always zero because magnetic force changes only the direction of motion, not the speed.